Solve 49/75*2/3/frac{49{75}*2/3+frac{1}{300}*frac{1}{3}}

$$\frac { \frac { 49 } { 75 } \times \frac { 2 } { 3 } } { \frac { 49 } { 75 } \times \frac { 2 } { 3 } + \frac { 1 } { 300 } \times \frac { 1 } { 3 } }$$

Evaluate

$$\frac{392}{393}\approx 0.997455471$$

Solution Steps

Multiply \frac{49}{75} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{49\times 2}{75\times 3}}{\frac{49}{75}\times \frac{2}{3}+\frac{1}{300}\times \frac{1}{3}}$$

Do the multiplications in the fraction \frac{49\times 2}{75\times 3}.

$$\frac{\frac{98}{225}}{\frac{49}{75}\times \frac{2}{3}+\frac{1}{300}\times \frac{1}{3}}$$

Multiply \frac{49}{75} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{98}{225}}{\frac{49\times 2}{75\times 3}+\frac{1}{300}\times \frac{1}{3}}$$

Do the multiplications in the fraction \frac{49\times 2}{75\times 3}.

$$\frac{\frac{98}{225}}{\frac{98}{225}+\frac{1}{300}\times \frac{1}{3}}$$

Multiply \frac{1}{300} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{98}{225}}{\frac{98}{225}+\frac{1\times 1}{300\times 3}}$$

Do the multiplications in the fraction \frac{1\times 1}{300\times 3}.

$$\frac{\frac{98}{225}}{\frac{98}{225}+\frac{1}{900}}$$

Least common multiple of 225 and 900 is 900. Convert \frac{98}{225} and \frac{1}{900} to fractions with denominator 900.

$$\frac{\frac{98}{225}}{\frac{392}{900}+\frac{1}{900}}$$

Since \frac{392}{900} and \frac{1}{900} have the same denominator, add them by adding their numerators.

$$\frac{\frac{98}{225}}{\frac{392+1}{900}}$$

Add 392 and 1 to get 393.

$$\frac{\frac{98}{225}}{\frac{393}{900}}$$

Reduce the fraction \frac{393}{900} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{98}{225}}{\frac{131}{300}}$$

Divide \frac{98}{225} by \frac{131}{300} by multiplying \frac{98}{225} by the reciprocal of \frac{131}{300}.

$$\frac{98}{225}\times \frac{300}{131}$$

Multiply \frac{98}{225} times \frac{300}{131} by multiplying numerator times numerator and denominator times denominator.

$$\frac{98\times 300}{225\times 131}$$

Do the multiplications in the fraction \frac{98\times 300}{225\times 131}.

$$\frac{29400}{29475}$$

Reduce the fraction \frac{29400}{29475} to lowest terms by extracting and canceling out 75.

$$\frac{392}{393}$$

Factor

$$\frac{2 ^ {3} \cdot 7 ^ {2}}{3 \cdot 131} = 0.9974554707379135$$